Update on SPS BPM impedance B. Salvant for the 2008 impedance team
Reference: http://cdsweb.cern.ch/record/1208424/files/CERN-ATS-2009-046.pdf • 106 BPH and 96 BPV in the SPS • Low frequency imaginary impedance for a BPH :Zlong/n ~ 1 mΩ, Zx=- 0.1 kΩ/m and Zy=2 kΩ/m. • Separate simulations for a BPV: Zlong/n~0.5mΩ, Zy= 0.1 kΩ/m and Zx= 0.2 kΩ/m.
Modelled structure for the BPH Ultrarelativistic beams All materials are perfect conductors (except the ceramic spacers) In fact: - Electrodes + pipe should be inStainless Steel - Casing should be in Anticorodal Rs=|V|^2/Plosses
BPH horizontal (with material losses) Quite insignificant change of transverse displacement on shunt impedance
BPV (with material losses) Longitudinal vertical horizontal
Effect on the beam Headtail simulations • Simulations done at the time with small longitudinal emittance (0.15 eVs) • All BPMs are lumped in one location accounting for the respective beta functions. • Linear longitudinal restoring force • No direct space charge
Summary • Effect of impedance of BPH and BPV is small on transverse single bunch dynamics • Longitudinal modes : • Rs~1 to 10 k Ω • R/Q~ 5 to 20 Ω • Larger for BPHs than BPVs • Frequencies above 1 GHz • Transverse modes: • Modes at 0.5 GHz (vertical for BPH) and 0.7 GHz (horizontal for BPV) • Rs~1 to 20 kΩ/m • R/Q~ 5 to 50 Ω/m
Effect of matching the impedance at electrodes coaxial ports in Particle Studio simulations (BPH) Modes are damped by the “perfect matching layer” at the coaxial port Short bunch (1 cm rms) SPS bunch (20 cm rms) Electrodecoaxial port Importance to match the BPM electrodes!
BPH Longitudinal vertical horizontal
Longitudinal Time domain (CST PS) Frequency domain eigenmode solver at the peaks (CST MWS)
Longitudinal (with losses) Electrodes + pipe Stainless Steel Casing Anticorodal